Question

数学解方程(x/x-2)+(x-9/x-7)=(x+1/x-1)+(x-8/x-6)

Answer 1

原式=1+2/(x-2)+1-2(x-7)=1+2/(x-1)+1-2/(x-6)（x/(x-2)=(x-2+2)/(x-2)=1+2/(x-2)，将所有分子上的x去掉）

=1/(x-2)-1/(x-7)=1/(x-1)-1/(x-6)
=-5/(x-2)(x-7)=-5/(x-1)(x-6)
(x-2)(x-7)=(x-1)(x-6)
-9x+14=-7x+6
2x=8
x=4
思路如上，希望没有出现计算错误，请自己按思路计算一遍。

Answer 2

1.x/(x-2)=1+2/(x-2)
x-9/(x-7)=
1-2/(x-7)
x+1/(x-1)=1+2/(x-1)
x-8/(x-6)=1-2/(x-6)
代入得1/(x-2)-1/(x-7)=1/(x-1)-1/(x-6)
移项得1/(x-2)+1/(x-6)=1/(x-1)+1/(x-7)
然后通分就好算了，注意x不等于1,2,6,7(分母不为0),最后要作为增根消去.
2.方法类似上一题,都是先写成1+一个分数的形式,然后移项后再通分